Lab 10 - Metaheuristics¶

Information on group members:

  1. 150284, Sofya Aksenyuk
  2. 150281, Uladzimir Ivashka
In [1]:
import numpy as np
import matplotlib.pyplot as plt
import random
import pandas as pd
import warnings
from tqdm import tqdm
warnings.filterwarnings("ignore")
  1. Given below is a benchmark objective function to be maximized. It can be parameterized to be 2, 3, 4, or 5 dimensional (M parameter). Implement any heuristic shown during the lecture to find the optimum. Your study should involve:
  • sensitivity analysis concerning the number of objectives involved;
  • sensitivity analysis concerning different ways of parameterizing your algorithm (e.g., population size in an evolutionary algorithm);
  • for each experimental setting, the method should be run multiple times, and the obtained results should be averaged;
  • consider presenting the results using tables and plots.
In [2]:
def getF(P):
    M = len(P)
    refPoints = [
 [[0.7, 0.3], [0.2, 0.2], [0.3, 0.6], [0.7, 0.9], [0.35, 0.35], [0.6, 0.6], [0.2, 0.9]], #M = 2
 [[0.7, 0.3, 0.5], [0.2, 0.2, 0.1], [0.3, 0.6, 0.9], [0.7, 0.9, 0.2], [0.35, 0.35, 0.35], [0.6, 0.6, 0.6], [0.2, 0.9, 0.4]], #M = 3
 [[0.7, 0.3, 0.5, 0.9], [0.2, 0.2, 0.1, 0.2], [0.3, 0.6, 0.9, 0.5], [0.7, 0.9, 0.2, 0.4], [0.35, 0.35, 0.35, 0.35], [0.6, 0.6, 0.6, 0.6], [0.2, 0.9, 0.4, 0.1]], #M = 4
 [[0.7, 0.3, 0.5, 0.9, 0.2], [0.2, 0.2, 0.1, 0.2, 0.6], [0.3, 0.6, 0.9, 0.5, 0.1], [0.7, 0.9, 0.2, 0.4, 0.9], [0.35, 0.35, 0.35, 0.35, 0.2], [0.6, 0.6, 0.6, 0.6, 0.9], [0.2, 0.9, 0.4, 0.1, 0.5]] #M = 5
    ]
    
    PP = np.array(P)
    v = 2.5*np.exp(-(5*np.linalg.norm(PP - np.array(refPoints[M-2][0])))**2)
    v += 1.0*np.exp(-(6*np.linalg.norm(PP - np.array(refPoints[M-2][1])))**2)
    v += 1.5*np.exp(-(6*np.linalg.norm( PP - np.array(refPoints[M-2][2])))**2)
    v += 1.2*np.exp(-(3*np.linalg.norm( PP - np.array(refPoints[M-2][3])))**2)
    v += 1.7*np.exp(-(14*np.linalg.norm( PP - np.array(refPoints[M-2][4])))**2)
    v += 1.4*np.exp(-(6.5*np.linalg.norm( PP - np.array(refPoints[M-2][5])))**2)
    v += 2.0*np.exp(-(10.0*np.linalg.norm( PP - np.array(refPoints[M-2][6])))**2)
    return v

print(getF([0.7, 0.3, 0.5]))

2.5343274543723906
In [3]:
def generate_population(popsize, dims=None):
    population = []
    if dims is None:
        for dim in [2, 3, 4, 5]:
            population += [np.random.normal(size=dim) for _ in range(popsize//4)]
    else:
        population += [np.random.normal(size=dims) for _ in range(popsize)]
        
    return sorted(population, key=getF, reverse=True)
In [4]:
def change_dimensions(gen):
    if np.random.randint(0, 100) < 10:
        if len(gen) == 2:
            gen.append(np.random.normal())
        elif len(gen) == 5:
            gen.pop(np.random.choice(range(len(gen))))
        else:
            if np.random.randint(0, 100) < 50:
                gen.append(np.random.normal())
            else:
                gen.pop(np.random.choice(range(len(gen))))
    return gen
In [5]:
def mutate(gen, prob=50, div=10, change_dim=False):
    gen = list(gen)
    for idx in range(len(gen)):
        if np.random.randint(0, 100) < prob:
            gen[idx] += np.random.normal() / div
    
    ## change dimensions
    if change_dim:
        gen = change_dimensions(gen)
    
    return np.array(gen)
In [6]:
def crossover(gen1, gen2):
    cut_point = max(len(gen1), len(gen2)) // 2
    gen1, gen2 = list(gen1), list(gen2)
    child = gen1[:cut_point] + gen2[cut_point:] if np.random.randint(0, 100) < 50 else gen2[:cut_point] + gen1[cut_point:]
    return np.array(child)
In [7]:
def tournament_selection(population, k):
    tournament = random.choices(population, k=k)
    return np.array(max(tournament, key=getF))
In [8]:
def evolve(population, popsize, tournament_size, _print=False, change_dim=False):
    bests = []
    prev_best_score = 0
    counter = 0
    
    while True:
        ## mutation of bad ones
        for bad_gen in population[int(0.9*popsize):popsize][::-1]:
            bad_gen = mutate(bad_gen, change_dim)
            population.append(bad_gen)
        ## crossover
        for _ in range(int(0.5*popsize)):
            parent1 = tournament_selection(population, tournament_size)
            parent2 = tournament_selection(population, tournament_size)
            child = crossover(parent1, parent2)
            population.append(child)
        ## mutation
        for _ in range(int(0.5*popsize)):
            winner = tournament_selection(population, tournament_size)
            winner = mutate(winner, change_dim)
            population.append(winner)
        ## some new random samples
        population += generate_population(int(0.1*popsize))

        population = sorted(population, key=getF, reverse=True)
        population = population[:popsize]
        
        best_score = getF(population[0])
        bests.append(best_score)
        if best_score == prev_best_score:
            counter += 1
        else:
            counter = 0
            prev_best_score = best_score
            
        if _print:
            print(f'Best gen: {population[0]}; score: {best_score}')
        
        if counter > 100:
            break
        
    return bests

Example of evolution¶

Population of mixed dimensions with change of dimensions in mutation¶

In [9]:
population = generate_population(100)
print(f'Best gen: {population[0]}, score: {getF(population[0])}')
_ = evolve(population, 100, 5, _print=True, change_dim=True)

Best gen: [0.16249393 0.89564664], score: 1.8560173611999966
Best gen: [0.16249393 0.89564664]; score: 1.8560173611999966
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.22024594 0.89564664]; score: 2.1185914554693515
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89564664]; score: 2.1645092154218233
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.20926374 0.89652864]; score: 2.164989696155189
Best gen: [0.63974192 0.36402125]; score: 2.2763139735333837
Best gen: [0.66373647 0.28799297]; score: 2.4711894906622005
Best gen: [0.66373647 0.28799297]; score: 2.4711894906622005
Best gen: [0.66373647 0.28799297]; score: 2.4711894906622005
Best gen: [0.66373647 0.28799297]; score: 2.4711894906622005
Best gen: [0.66373647 0.28799297]; score: 2.4711894906622005
Best gen: [0.66373647 0.28799297]; score: 2.4711894906622005
Best gen: [0.66373647 0.28799297]; score: 2.4711894906622005
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.66373647 0.31558897]; score: 2.498965849502964
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31558897]; score: 2.528548975404434
Best gen: [0.67174351 0.31421768]; score: 2.5290356800511757
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31421768]; score: 2.5554225360556893
Best gen: [0.71413896 0.31105206]; score: 2.556675529807993
Best gen: [0.71413896 0.31105206]; score: 2.556675529807993
Best gen: [0.71413896 0.31105206]; score: 2.556675529807993
Best gen: [0.71413896 0.31105206]; score: 2.556675529807993
Best gen: [0.71413896 0.31105206]; score: 2.556675529807993
Best gen: [0.71413896 0.31105206]; score: 2.556675529807993
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.71413896 0.30861031]; score: 2.5569167133378254
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.70596532 0.30861031]; score: 2.5690353712212537
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.30861031]; score: 2.5712476849643506
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69324268 0.31122767]; score: 2.571257486000921
Best gen: [0.69484495 0.31122767]; score: 2.572074501361523
Best gen: [0.69484495 0.31122767]; score: 2.572074501361523
Best gen: [0.69484495 0.31122767]; score: 2.572074501361523
Best gen: [0.69484495 0.31122767]; score: 2.572074501361523
Best gen: [0.69484495 0.31122767]; score: 2.572074501361523
Best gen: [0.69484495 0.31122767]; score: 2.572074501361523
Best gen: [0.69484495 0.31122767]; score: 2.572074501361523
Best gen: [0.69587387 0.31122767]; score: 2.5724291996794166
Best gen: [0.69587387 0.31122767]; score: 2.5724291996794166
Best gen: [0.69587387 0.31122767]; score: 2.5724291996794166
Best gen: [0.69587387 0.31122767]; score: 2.5724291996794166
Best gen: [0.69587387 0.31122767]; score: 2.5724291996794166
Best gen: [0.69587387 0.31122767]; score: 2.5724291996794166
Best gen: [0.69587387 0.31122767]; score: 2.5724291996794166
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.31122767]; score: 2.5727219429188954
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403
Best gen: [0.69865995 0.30987997]; score: 2.5728488178148403

Population of a singe dimension without change of dimensions in mutation (2D as an example)¶

In [10]:
population = generate_population(100, dims=2)
print(f'Best gen: {population[0]}, score: {getF(population[0])}')
_ = evolve(population, 100, 5, _print=True)

Best gen: [0.57870912 0.49640246], score: 1.8376210988207293
Best gen: [0.57870912 0.49640246]; score: 1.8376210988207293
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067
Best gen: [0.57870912 0.62900951]; score: 2.072682103411067

Plots¶

In [11]:
df = pd.DataFrame([])
In [12]:
def plot_comparisons(df, dims=None):
    plt.rcParams["figure.figsize"] = (25,10)
    plt.rcParams.update({'font.size': 18, 'font.family': 'Tahoma'})
    
    results_avg = {}
    results_len = {}
    for popsize in tqdm(range(50, 250, 50)):
        if not dims:
            population = generate_population(popsize)
        else:
            population = generate_population(popsize, dims)
        for tournament_size in [1, 2, 5, 10]:
            temp_avg = []
            temp_len = []
            for _ in range(10):
                if not dims:
                    res = evolve(population, popsize, tournament_size, change_dim=True)
                else:
                    res = evolve(population, popsize, tournament_size)
                temp_avg.append(res[-1])
                temp_len.append(len(res))
            results_avg[(popsize, tournament_size)] = sum(temp_avg) / len(temp_avg)
            results_len[(popsize, tournament_size)] = sum(temp_len) / len(temp_len)  

    label = 'mixed dims' if not dims else f'{dims}D'
    plt.bar(height=list(results_avg.values()), x=range(len(results_avg)))
    plt.title(f"Best fitness comparison, {label}")
    plt.xlabel("Parameters (popsize, k)")
    plt.ylabel("Best fitness value")
    plt.xticks(range(len(results_avg)), labels=list(results_avg.keys()), rotation = 90)
    plt.show()

    plt.bar(height=list(results_len.values()), x=range(len(results_len)))
    plt.title(f"No. of iterations comparison, {label}")
    plt.xlabel("Parameters (popsize, k)")
    plt.ylabel("No. of iterations")
    plt.xticks(range(len(results_len)), labels=list(results_len.keys()), rotation = 90)
    plt.show()
    
    df_temp = pd.DataFrame({f'Parameters {label}': list(results_avg.keys()),
                            f'Best fitness {label}':  list(results_avg.values()),
                            f'Iterations {label}': list(results_len.values())})
    return df_temp

Population of mixed dimensions with change of dimensions in mutation¶

In [13]:
df_temp = plot_comparisons(df=df)
df = pd.concat([df, df_temp], axis=1)

100%|███████████████████████████████████████████████████████████████████████████████████| 4/4 [42:06<00:00, 631.61s/it]
In [14]:
df
Out[14]:
Parameters mixed dims Best fitness mixed dims Iterations mixed dims
0 (50, 1) 2.572099 167.0
1 (50, 2) 2.572474 213.7
2 (50, 5) 2.572232 164.6
3 (50, 10) 2.571771 163.2
4 (100, 1) 2.572753 240.2
5 (100, 2) 2.572485 218.9
6 (100, 5) 2.572703 233.9
7 (100, 10) 2.572609 239.0
8 (150, 1) 2.572839 260.1
9 (150, 2) 2.572803 246.0
10 (150, 5) 2.572726 210.4
11 (150, 10) 2.572783 238.6
12 (200, 1) 2.572839 217.2
13 (200, 2) 2.572836 293.8
14 (200, 5) 2.572831 248.7
15 (200, 10) 2.572783 233.6

Population of a singe dimension without change of dimensions in mutation¶

In [15]:
for dim in range(2, 6):
    df_temp = plot_comparisons(df, dim)
    df = pd.concat([df, df_temp], axis=1)

100%|███████████████████████████████████████████████████████████████████████████████████| 4/4 [20:18<00:00, 304.72s/it]

100%|███████████████████████████████████████████████████████████████████████████████████| 4/4 [21:17<00:00, 319.34s/it]

100%|███████████████████████████████████████████████████████████████████████████████████| 4/4 [21:06<00:00, 316.50s/it]

100%|███████████████████████████████████████████████████████████████████████████████████| 4/4 [22:05<00:00, 331.34s/it]
In [16]:
df
Out[16]:
Parameters mixed dims Best fitness mixed dims Iterations mixed dims Parameters 2D Best fitness 2D Iterations 2D Parameters 3D Best fitness 3D Iterations 3D Parameters 4D Best fitness 4D Iterations 4D Parameters 5D Best fitness 5D Iterations 5D
0 (50, 1) 2.572099 167.0 (50, 1) 2.421950 118.7 (50, 1) 2.068911 130.3 (50, 1) 2.333243 119.9 (50, 1) 2.221048 182.1
1 (50, 2) 2.572474 213.7 (50, 2) 2.572166 103.6 (50, 2) 2.032668 152.7 (50, 2) 2.188085 142.3 (50, 2) 2.221174 153.3
2 (50, 5) 2.572232 164.6 (50, 5) 2.572166 102.0 (50, 5) 2.147977 117.4 (50, 5) 2.243236 141.4 (50, 5) 1.978642 136.5
3 (50, 10) 2.571771 163.2 (50, 10) 2.572166 102.0 (50, 10) 2.275386 111.1 (50, 10) 2.545728 102.1 (50, 10) 2.213248 152.8
4 (100, 1) 2.572753 240.2 (100, 1) 2.377773 135.6 (100, 1) 2.379755 145.7 (100, 1) 2.472010 121.0 (100, 1) 2.313324 152.3
5 (100, 2) 2.572485 218.9 (100, 2) 2.409922 123.5 (100, 2) 2.276762 136.4 (100, 2) 2.521331 104.5 (100, 2) 2.441731 110.3
6 (100, 5) 2.572703 233.9 (100, 5) 2.243520 125.1 (100, 5) 2.415446 121.0 (100, 5) 2.439718 117.2 (100, 5) 2.361770 155.2
7 (100, 10) 2.572609 239.0 (100, 10) 2.426253 134.2 (100, 10) 2.546262 103.0 (100, 10) 2.519614 103.0 (100, 10) 2.521963 102.6
8 (150, 1) 2.572839 260.1 (150, 1) 2.505649 107.6 (150, 1) 2.473216 141.9 (150, 1) 2.443675 139.2 (150, 1) 2.409164 139.8
9 (150, 2) 2.572803 246.0 (150, 2) 2.537076 115.3 (150, 2) 2.433891 135.9 (150, 2) 2.454604 122.3 (150, 2) 2.435611 123.9
10 (150, 5) 2.572726 210.4 (150, 5) 2.549279 108.2 (150, 5) 2.414072 112.4 (150, 5) 2.464903 102.9 (150, 5) 2.430410 120.5
11 (150, 10) 2.572783 238.6 (150, 10) 2.564389 102.2 (150, 10) 2.439341 128.3 (150, 10) 2.468528 111.4 (150, 10) 2.558271 116.6
12 (200, 1) 2.572839 217.2 (200, 1) 2.556187 123.6 (200, 1) 2.531470 114.4 (200, 1) 2.408965 156.6 (200, 1) 2.540959 130.8
13 (200, 2) 2.572836 293.8 (200, 2) 2.560163 105.3 (200, 2) 2.560042 110.3 (200, 2) 2.445352 126.4 (200, 2) 2.542073 124.7
14 (200, 5) 2.572831 248.7 (200, 5) 2.572617 103.5 (200, 5) 2.511060 107.6 (200, 5) 2.526423 127.1 (200, 5) 2.537514 103.7
15 (200, 10) 2.572783 233.6 (200, 10) 2.572617 103.0 (200, 10) 2.560292 103.9 (200, 10) 2.537441 102.6 (200, 10) 2.548734 107.6
In [17]:
def popsize_influence(dims=None):
    plt.rcParams["figure.figsize"] = (20,10)
    plt.rcParams.update({'font.size': 18, 'font.family': 'Tahoma'})

    for popsize in range(50, 250, 50):
        results = {}
        iters = []
        if not dims:
            population = generate_population(popsize)
        else:
            population = generate_population(popsize, dims)
        for tournament_size in [1, 2, 5, 10]:
            if not dims:
                res = evolve(population, popsize, tournament_size, change_dim=True)
            else:
                res = evolve(population, popsize, tournament_size)
            results[str(tournament_size)] = res
            iters.append(len(res))

        for size, res in results.items():
            plt.plot(res, label=f"Tournament size: {size}")
        plt.title(f"Population size of {popsize}")
        plt.xlabel(f"No. of generations, total: {max(iters)}")
        plt.ylabel("Fitness value")
        plt.legend()
        plt.xlim(0, 20)
        plt.show()
Note: (x-axis is limited to be seen better)¶

Population of mixed dimensions with change of dimensions in mutation¶

In [18]:
popsize_influence()

Population of single dimension without change of dimensions in mutation¶

In [19]:
for dim in range(2, 6):
    popsize_influence(dim)
In [20]:
def tournament_size_influence(dims=None):
    plt.rcParams["figure.figsize"] = (20,10)
    plt.rcParams.update({'font.size': 18, 'font.family': 'Tahoma'})

    for tournament_size in [1, 2, 5, 10]:
        results = {}
        iters = []
        for popsize in range(50, 250, 50):
            if not dims:
                population = generate_population(popsize)
            else:
                population = generate_population(popsize, dims)
            if not dims:
                res = evolve(population, popsize, tournament_size, change_dim=True)
            else:
                res = evolve(population, popsize, tournament_size)   
            results[str(popsize)] = res
            iters.append(len(res))

        for popsize, res in results.items():
            plt.plot(res, label=f"Population size: {popsize}")
        plt.title(f"Tournament size of {tournament_size}")
        plt.xlabel(f"No. of generations, total: {max(iters)}")
        plt.ylabel("Fitness value")
        plt.legend()
        plt.xlim(0, 20)
        plt.show()
Note: (x-axis is limited to be seen better)¶

Population of mixed dimensions with change of dimensions in mutation¶

In [21]:
tournament_size_influence()

Population of single dimension without change of dimensions in mutation¶

In [22]:
for dim in range(2, 6):
    tournament_size_influence(dim)